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On the additive groups of subdirectly irreducible rings

Published online by Cambridge University Press:  17 April 2009

Yasuyuki Hirano  and
Isao Mogami
Yasuyuki Hirano
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
Isao Mogami
Affiliation:
Tsuyama College of Technology, Tsuyama 708, Department of Mathematics, Okayama University, Okayama 700, Japan
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Abstract

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In this paper we study the additive group structure of subdirectly irreducible rings and their hearts. We give and example of a torsion-free, non-reduced abelian group which is not the underlying additive group of any associative subdirectly irreducible ring. It is a counterexample to a theorem in Feigelstock's book “Additive Groups of Rings.”

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 275 - 281
Copyright
Copyright © Australian Mathematical Society 1986

References

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